Dynamic impact experiments based on high-speed photography and digital image correlation (DIC) techniques were carried out on sandstone specimens containing arched holes to investigate the effect of the incident angle. In addition, the complex function method based on conformal mapping was used to theoretically calculate the transient dynamic stress distributions around the arched holes. The test results indicated that the strength and modulus of elasticity of the specimens under dynamic impact decreased and then increased with the increase of the inclination angle of the holes from 0 to 90° at intervals of 15°, reaching a minimum value at 60°, due to the large stress concentration at this angle leading to the shear failure of the specimen. During the experiment, rock debris ejections, spalling, and heaving were observed around the holes, and the rock debris ejections served as an indicator to identify the early fracture. The damage mechanism around the holes was revealed theoretically, i.e., the considerable compressive stress concentration in the perpendicular incidence direction around the arched hole and the tensile stress concentration on the incidence side led to the initiation of the damage around the cavity, and the theoretical results were in satisfactory agreement with the experimental results. In addition, the effect of the initial stress on the dynamic response of the arched tunnel was discussed.